Explicit expressions for European option pricing under a generalized skew normal distribution

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Under a generalized skew normal distribution we consider the problem of European option pricing. Existence of the martingale measure is proved. An explicit expression for a given European option price is presented in terms of the cumulative distribution function of the univariate skew normal and the bivariate standard normal distributions. Some special cases are investigated in a greater detail. To carry out the sensitivity of the option price to the skew parameters, numerical methods are applied. Some concluding remarks and further works are given. The results obtained are extensions of the results provided by [4].